Details

sample56.0ms

Algorithm

intervals

Results

12.0ms	33×	body	2560	valid
10.0ms	39×	body	1280	valid
9.0ms	166×	body	80	valid
4.0ms	22×	body	640	valid
4.0ms	77×	body	80	nan
2.0ms	12×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 35.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.6b	(- (* b b) (* (* 4.0 a) c))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune241.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 4.4b

Counts

83 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.0b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

9.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
17.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series475.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
146.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
182.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	651	2694
1	3139	2439
2	5002	2426

prune387.0ms

Filtered

166 candidates to 111 candidates (66.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	165	8	173

Merged error: 4.4b

Counts

173 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

5.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
8.0b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))))
14.3b	(- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
102×	`times-frac`
86×	`*-un-lft-identity`
42×	`add-cube-cbrt`
33×	`associate-/l*` `difference-of-squares`
22×	`log-prod` `exp-sum` `distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
9×	`associate-/r*`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 165

Calls

4 calls:

23.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
16.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))))
11.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
182.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))))
74.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	698	3374
1	3196	2930
2	5001	2873

prune477.0ms

Filtered

177 candidates to 115 candidates (65.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	177	8	185

Merged error: 4.4b

Counts

185 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
0.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.4b	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`flip3--` `sqrt-prod` `flip--`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `associate-*r/` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 72

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
148.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	485	952
1	2854	745
2	5001	737

prune188.0ms

Filtered

84 candidates to 58 candidates (69.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	85	7	92

Merged error: 4.4b

Counts

92 → 7

regimes157.0ms

Accuracy

93% (1.7b remaining)

Error of 7.2b against oracle of 5.5b and baseline of 29.8b

bsearch138.0ms

Steps

Iters	Range	Point
7	3.0106008231332273e+28	3.853441604264477e+30	3.7841174599135035e+30
8	-2.927933099620566e-203	-2.4110032972616562e-207	-2.8254292841125695e-206
2	-4.193597519284562e+95	-3.5355996581575456e+95	-4.111347786643685e+95

Iters

Range

Point

3.0106008231332273e+28

3.853441604264477e+30

3.7841174599135035e+30

-2.927933099620566e-203

-2.4110032972616562e-207

-2.8254292841125695e-206

-4.193597519284562e+95

-3.5355996581575456e+95

-4.111347786643685e+95

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	28
1	50	28
2	50	28

end0.0ms

sample1.5s

Algorithm

intervals

Results

344.0ms	1132×	body	2560	valid
314.0ms	5781×	body	80	valid
220.0ms	895×	body	1280	valid
150.0ms	2866×	body	80	nan
90.0ms	466×	body	640	valid
41.0ms	107×	body	5120	valid
36.0ms	247×	body	320	valid
11.0ms	109×	body	160	valid